Physics – Condensed Matter – Statistical Mechanics
Scientific paper
2004-05-18
Physics
Condensed Matter
Statistical Mechanics
28 pages, submitted to J. Math. Phys --
Scientific paper
10.1063/1.1874332
Landscape paradigm is ubiquitous in physics and other natural sciences, but it has to be supplemented with both quantitative and qualitatively meaningful tools for analyzing the topography of a given landscape. We here consider dynamic explorations of the relief and introduce as basic topographic features ``wells of duration $T$ and altitude $y$''. We determine an intrinsic exploration mechanism governing the evolutions from an initial state in the well up to its rim in a prescribed time, whose finite-difference approximations on finite grids yield a constructive algorithm for determining the wells. Our main results are thus (i) a quantitative characterization of landscape topography rooted in a dynamic exploration of the landscape, (ii) an alternative to stochastic gradient dynamics for performing such an exploration, (iii) a constructive access to the wells and (iv) the determination of some bare dynamic features inherent to the landscape. The mathematical tools used here are not familiar in physics: They come from set-valued analysis (differential calculus of set-valued maps and differential inclusions) and viability theory (capture basins of targets under evolutionary systems) which have been developed during the last two decades; we therefore propose a minimal appendix exposing them at the end of this paper to bridge the possible gap.
Aubin Jean-Pierre
Lesne Annick
No associations
LandOfFree
Constructing and exploring wells of energy landscapes does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with Constructing and exploring wells of energy landscapes, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Constructing and exploring wells of energy landscapes will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-365849